Question

k为何值时,x^2-4xy+4y^2-10x+20y+k^2+9是一个完全平方式?

Answer 1

x^2-4xy+4y^2-10x+20y+k^2+9

=(x-2y)^2-10(x-2y)+(k^2+9)

k^2+9=(10/2)^2=25

k^2=16

k1=4,k2=-4.

k为4或-4时,x^2-4xy+4y^2-10x+20y+k^2+9是一个完全平方式.